Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal of Mathematical Physics

Quantum information geometry and standard purification

Anna Jenčová

Published May 1, 2002• 13 citations
Publisher

Abstract

We investigate relations between Uhlmann’s parallelism, monotone Riemannian metrics and dual affine connections on the space of density matrices.
DOI
10.1063/1.1467966

Related papers

Computation of Uhlmann's parallel transport for density matrices and the Bures metric on three-dimensional Hilbert space

Matthias Hübner

Physics Letters A•Aug 1, 1993•128 citations

On the Riemannian metric on the space of density matrices

Jochen Dittmann

Reports on Mathematical Physics•Oct 1, 1995•32 citations

Generalization of quantum monotonic metric with duality via a purification

Kouta Sakurai, Tomohiro Ogawa

IEICE Technical Report; IEICE Tech. Rep.•Nov 24, 2020•0 citations

Dualistic properties of the manifold of quantum states

Anna Jenčová

In the finite dimensional case, we introduce a family of torsion-free affine connections in the manifold of all invertible density matrices. These are the quantum version of Amari’s α-connections, based on the α-representation of the tangent space. The dual connections with respect to a monotone metric are, in general, not torsion-free. We compute the torsion and the Riemannian curvature. Finally, geodesics are used to define a divergence.

AIP conference proceedings•Jan 1, 2001•4 citations

ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY

Matheus R. Grasselli, R. F. Streater

We show that, in finite dimensions, the only monotone metrics on the space of invertible density matrices for which the (+1) and (-1) affine connections are mutually dual are constant multiples of the Bogoliubov–Kubo–Mori metric.

arXiv:math-ph/0006030•Infinite Dimensional Analysis Quantum Probability and Related Topics•Jun 1, 2001•40 citations

Metrics of unitary matrices and their applications in quantum information theory

Kai-yan Lee

•Jan 1, 2011•1 citation